The following operations are always available for ring elements. Of course the operands must lie in compatible rings, i.e., the rings must be equal, or at least have a common superring.
r + s
The operator + evaluates to the sum of the two ring elements r and
s, which must lie in compatible rings.
r - s
The operator - evaluates to the difference of the two ring elements
r and s, which must lie in compatible rings.
r * s
The operator * evaluates to the product of the two ring elements r
and s, which must lie in compatible rings.
r ^ n
The operator ^ evaluates to the n-th power of the ring element r.
If n is a positive integer then r^n is r*r*..*r
(n factors). If n is a negative integer r^n is defined as
1 / {<r>^{-<n>}}. If 0 is raised to a negative power an error is
signalled. Any ring element, even 0, raised to the 0-th power yields 1.
For the precedence of the operators see Operations.
Note that the quotient operator / usually performs the division in the
quotient field of the ring. To compute a quotient in a ring use the
function Quotient (see Quotient).
GAP 3.4.4